5y(2y-3)+(2y-3)=0

Solution for 5y(2y-3)+(2y-3)=0 equation:

Simplifying
5y(2y + -3) + (2y + -3) = 0

Reorder the terms:
5y(-3 + 2y) + (2y + -3) = 0
(-3 * 5y + 2y * 5y) + (2y + -3) = 0
(-15y + 10y2) + (2y + -3) = 0

Reorder the terms:
-15y + 10y2 + (-3 + 2y) = 0

Remove parenthesis around (-3 + 2y)
-15y + 10y2 + -3 + 2y = 0

Reorder the terms:
-3 + -15y + 2y + 10y2 = 0

Combine like terms: -15y + 2y = -13y
-3 + -13y + 10y2 = 0

Solving
-3 + -13y + 10y2 = 0

Solving for variable 'y'.

Factor a trinomial.
(-1 + -5y)(3 + -2y) = 0

Subproblem 1
Set the factor '(-1 + -5y)' equal to zero and attempt to solve:

Simplifying
-1 + -5y = 0

Solving
-1 + -5y = 0

Move all terms containing y to the left, all other terms to the right.

Add '1' to each side of the equation.
-1 + 1 + -5y = 0 + 1

Combine like terms: -1 + 1 = 0
0 + -5y = 0 + 1
-5y = 0 + 1

Combine like terms: 0 + 1 = 1
-5y = 1

Divide each side by '-5'.
y = -0.2

Simplifying
y = -0.2
Subproblem 2
Set the factor '(3 + -2y)' equal to zero and attempt to solve:

Simplifying
3 + -2y = 0

Solving
3 + -2y = 0

Move all terms containing y to the left, all other terms to the right.

Add '-3' to each side of the equation.
3 + -3 + -2y = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -2y = 0 + -3
-2y = 0 + -3

Combine like terms: 0 + -3 = -3
-2y = -3

Divide each side by '-2'.
y = 1.5

Simplifying
y = 1.5
Solution
y = {-0.2, 1.5}